// Numbas version: finer_feedback_settings
{"name": "LM05 Determinant of a 2x2 matrix", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "LM05 Determinant of a 2x2 matrix", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p><b>The determinant of a 2x2 matrix:</b></p>\n<p>Calculate the determinant of the following 2X2 matrices.</p>", "advice": "<p><strong>Determinant</strong></p>\n<p>The detrminant of a 2x2 matrix can be calculated using the following process:</p>\n<p>$$<br/>\\begin{vmatrix}<br/>a &amp; b \\\\<br/>c &amp; d \\\\<br/>\\end{vmatrix} = ad-bc.<br/>$$</p>\n<p><strong>Example</strong></p>\n<p>For $A = \\var{nonzerodet2},$</p>\n<p>we have that,</p>\n<p>$$<br/>\\begin{vmatrix}<br/>\\var{nonzerodet2[0][0]} &amp; \\var{nonzerodet2[0][1]}\\\\<br/>\\var{nonzerodet2[1][0]} &amp; \\var{nonzerodet2[1][1]}\\\\<br/>\\end{vmatrix}=(\\var{nonzerodet2[0][0]})(\\var{nonzerodet2[1][1]}) - (\\var{nonzerodet2[0][1]})(\\var{nonzerodet2[1][0]}) =\\var{detnonzerodet2}&nbsp;<br/>$$&nbsp;</p>\n<p><strong><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/next-steps#Matrices\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></strong></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"nonzerodet1": {"name": "nonzerodet1", "group": "Ungrouped variables", "definition": "matrix([a[0],a[1]],[a[2],ceil(a[1]*a[2]/a[0]+random(1..4))])", "description": "", "templateType": "anything", "can_override": false}, "nonzerodet2": {"name": "nonzerodet2", "group": "Ungrouped variables", "definition": "matrix([b[0],b[1]],[b[2],ceil(b[1]*b[2]/b[0]+random(1..4))])", "description": "", "templateType": "anything", "can_override": false}, "zerodet1": {"name": "zerodet1", "group": "Ungrouped variables", "definition": "matrix([c[0],c[1]],[3*c[0],3*c[1]])", "description": "", "templateType": "anything", "can_override": false}, "zerodet2": {"name": "zerodet2", "group": "Ungrouped variables", "definition": "Matrix([2*c[0],5*c[0]],[2*c[1],5*c[1]])", "description": "", "templateType": "anything", "can_override": false}, "detnonzerodet2": {"name": "detnonzerodet2", "group": "Ungrouped variables", "definition": "det(nonzerodet2)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "repeat(random(-9..9 except 0),3)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "repeat(random(-9..9 except 0),3)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "repeat(random(-9..9 except 0),2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "nonzerodet1", "b", "nonzerodet2", "c", "zerodet1", "zerodet2", "detnonzerodet2"], "variable_groups": [{"name": "matrix notation", "variables": []}], "functions": {"Latexcodebits": {"parameters": [["m", "number"], ["n", "number"]], "type": "list", "language": "jme", "definition": "repeat(repeat('&',n-1)+['\\\\\\\\'],m-1)+[repeat('&',n-1)+['']]"}, "stringify": {"parameters": [["input", "list"]], "type": "string", "language": "javascript", "definition": "var output = '';\nvar i;\nfor (i = 0; i < input.length; i++) {\n  output += input[i];\n} \nreturn output;"}, "Latexcodebitsproductcalc": {"parameters": [["m", "number"], ["k", "number"], ["n", "number"]], "type": "anything", "language": "jme", "definition": "repeat(repeat(repeat('+',k-1)+['&'],n-1)+[repeat('+',k-1)+['\\\\\\\\']],m-1)+[repeat(repeat('+',k-1)+['&'],n-1)+[repeat('+',k-1)+['']]]"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "a)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$$<br/>A=\\var{nonzerodet2}<br/>$$</p>\n<p></p>\n<p>$<br/>\\text{What is the value of}\\begin{vmatrix}<br/>A<br/>\\end{vmatrix}?<br/>$</p>\n<p>answer:[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "nonzerodet2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{detnonzerodet2}", "maxValue": "{detnonzerodet2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "b)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$$<br/>m=\\var{zerodet1}<br/>$$</p>\n<p></p>\n<p>$<br/>\\text{What is the value of}\\begin{vmatrix}<br/>M<br/>\\end{vmatrix}?<br/>$<br/><br/>answer:[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "zerodet1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "resources": []}]}], "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}]}